bài giảng kinh tế vi mô tiếng anh ch4 consumer choice

1
Chapter 4
Consumer Choice
Key issues
1. properties of preferences
2. utility
3. budget constraint
4. consumer's constrained choice
Tastes
• individual tastes (preferences) determine
pleasure people derive from goods
• economists usually
• take tastes as given
• do not judge taste
Individual decision making
• consumers face constraints on their choices
• consumers maximize their pleasure from
consumption subject to constraints
• we want to predict behavior not judge i
Consumer’s problem
• consumer allocates money over goods: buys
a bundle or market basket of goods
• 2 possible theories of consumer behavior
• maximizing behavior
• random behavior (next chapter)
Assumptions about consumer
preferences
1. completeness
2. transitivity
3. more is better
2

Assumption 1: Completeness
• consumer can rank any two bundles of
goods
• only one of following is true: consumer
• prefers Bundle x to Bundle y
• prefers Bundle y to Bundle x
• is indifferent between them
Assumption 2: Transitivity
(rationality)
• consumer's preference over bundles is
consistent:
• if consumer prefers
• Bundle z to Bundle y and
• Bundle y to Bundle x
• then consumer prefers Bundle z to Bundle x
Economist’s transitivity
experiment
• Weinstein (1968)
• no subject knew the purpose of the experiment
• each given choices between 10 goods of equal
value, offered in all possible combinations of pairs
• $3 in cash
• 8-cup Wearever aluminum coffee percolator
• free pass to next 4 Saturday matinees at subject's
favorite motion picture theater
Results
• transitive responses
• 93.5% adults (≥ 18 years old)
• 79.2% children aged 9 to 12
• result may explain why political and

economic restrictions are placed on youths
Psychologists' transitivity
experiment
• Bradbury and Ross (1990)
• share of people who made intransitive choice
involving 3 colors:
• nearly 50% of 4 or 5 year olds
• 15% of 11-13 year olds
• 5% for adults
• novelty (a preference for a new color) is
responsible for most of the intransitive responses
• novelty effect is especially strong in children
Assumption 3: More is better
• more of a good is better than less of it
• good: commodity for which more is preferred
to less at least at some levels of consumption
• bad: something for which less is preferred to
more, such as pollution
• consumers are not satiated
3
Which assumptions are critical
for our model?
• completeness and transitivity assumptions
are crucial
• more-is-better assumption is included only
to simplify the analysis
Why do economists make the
more-is-better assumption?
• it appears to be true about most people
• with free disposal, you can't be worse off

with extra goods
• consumers only buy goods where this
condition is met (we'll show later)
Preference maps
• we summarize information about a Lisa’s
preferences using a graph
• we can rank some bundles using more-is-
better assumption
Figure 4.1a Bundles of Pizzas and Burritos Lisa Might Consume
B, Burritos
per semester
(a) Ranking Regions
302515
Z, Pizzas per semester
25
20
15
10
0
d
a
b
e
c
f
A
B
Indifference curve
• we ask Lisa to identify all the bundles that
give her the same amount of pleasure as

consuming bundle e
• her answer: Curve I in Figure 4.1b,
“Indifference Curve”
Figure 4.1b Bundles of Pizzas and Burritos Lisa Might Consume
B, Burritos
per semester
(b) Indifference Curve
302515
Z, Pizzas per semester
25
20
15
10
0
d
a
b
I
e
c
f
4
Indifference or preference map
• complete set of indifference curves that
summarize a consumer's tastes
• Figure 4.1c shows parallel curves, but they
need not be parallel
Figure 4.1c Bundles of Pizzas and Burritos Lisa Might Consume
B, Burritos
per semester

(c) Preference Map
302515
Z, Pizzas per semester
25
20
15
10
0
d
I
0
I
1
I
2
e
c
f
Indifference curve properties
1. bundles on indifference curves farther
from the origin are preferred to those on
indifference curves closer to the origin
2. there is an indifference curve through
every possible bundle
3. indifference curves cannot cross
4. indifference curves are “thin”
5. indifference curves slope down
Property 1: Better off on farther
indifference curves
• bundles on indifference curves farther from

the origin are preferred to those on
indifference curves closer to the origin
• by more is better assumption
Figure 4.1c Bundles of Pizzas and Burritos Lisa Might Consume
B, Burritos
per semester
(c) Preference Map
302515
Z, Pizzas per semester
25
20
15
10
0
d
I
0
I
1
I
2
e
c
f
Property 2: Indifference curve
through every possible bundle
• by completeness: consumer can compare any
bundle to another
• compared to a given bundle, some bundles are
• preferred,

• enjoyed equally
•inferior
• connecting bundles that give the same pleasure
produces an indifference curve that includes the
given bundle
5
Property 3: Indifference curves
cannot cross
• assume the opposite: two indifference
curves cross at Bundle e in Figure 4.2a.
• look for a contradiction
Figure 4.2a Impossible Indifference Curves
B, Burritos
per semester
(a) Crossing
Z, Pizzas per semester
I
1
I
0
a
b
e
Property 4: Indifference curves
are "thin"
• assume the opposite: suppose an
indifference curve were thick (Figure 4.2c).
• look for a contradiction
Figure 4.2c Impossible Indifference Curves
B, Burritos

per semester
a
b
(c) Thick
Z, Pizzas per semester
I
Property 5: Indifference curves
slope down
• assume the opposite: indifference curve I
slopes up in Figure 4.2b
• look for a contradiction
Figure 4.2b Impossible Indifference Curves
B, Burritos
per semester
(b) Upward Sloping
Z, Pizzas per semester
I
a
b
6
Willingness to substitute
• downward-sloping indifference curve ⇒
consumer is willing to substitute one good
for the other
• marginal rate of substitution (MRS) of
burritos (rise) for pizza (run), is slope of
indifference curve:
B
MRS
Z

∆
=
∆
MRS varies along the
indifference curve
• indifference curve bow away from the
origin (convex)
• indicates diminish marginal rates of
substitution (MRS)
Figure 4.3a Marginal Rate of Substitution
B, Burritos
per semester
(a) Indifference Curve Convex to the Origin
5
3
8
1
–1
1
1
2
0
–2
–
3
3456
Z, Pizzas per semester
a
b
c

d
I
Concave indifference curve
• if indifference curve bows toward the origin
(concave)
• then (implausibly) increasing MRS
Figure 4.3b Marginal Rate of Substitution
B, Burritos
per semester
(b) Indifference Curve Concave to the Origin
5
7
1
1
2
0
–2
–
3
3456
Z, Pizzas per semester
a
b
c
I
Perfect substitutes
• straight line indifference curves
• if slope is –1, MRS = 1 (Coke-Pepsi)
7
Figure 4.4a Perfect Substitutes, Perfect Complements,

Imperfect Substitutes
Coke, Cans
per week
(a) Perfect Substitutes
1234
Pepsi, Cans per week
1
0
2
3
4
I
1
I
2
I
3
I
4
Perfect complements
• right-angle indifference curves
• MRS = 0 (Coffee-Cream)
Figure 4.4b Perfect Substitutes, Perfect Complements,
Imperfect Substitutes
Ice cream,
Scoops per week
(b) Perfect Complements
123
Pie, Slices per week
1

2
3
0
I
1
I
2
I
3
a
d
ec
b
Imperfect substitutes
• convex indifference curves
• lies between the two extremes (straight and
right-angle indifference curves)
Figure 4.4c Perfect Substitutes, Perfect Complements,
Imperfect Substitutes
B, Burritos
per semester
(c) Imperfect Substitutes
Z, Pizzas per semester
I
Application: Food vs. clothing
• indifference curves of the average U.S.
consumer between food consumed at home
and clothing
• as we move away from the origin:
• I

1
near right angles (perfect complements)
• I
4
near straight lines (perfect substitutes)
• why: minimum levels of food and clothing
are necessary to support life
8
Indifference Curves Between Food and Clothing
Food at home
per year
Clothing per year
I
4
I
3
I
2
I
1
Utility
• numerical value that reflects relative rankings of
various bundles of goods
• if Lisa prefers bundle a to b, then utility from a >
utility from b
• utility function:
• relationship between utility measure and every possible
bundle of good
• succinct summary of information in indifference map
Ordinal preference

• ordinal scale maintains only ranking:
• letter grades
• utility
• cardinal scale maintains ranking and allows
absolute comparisons: money payments
Utility and indifference curves
• could plot utility and two goods in a 3D
figure: hill of happiness
• indifference curves are determined by
taking parallel cuts of the hill of happiness
at some given level of utility
Utility and marginal utility
• marginal utility of Z
• change in utility from a small increase in Z
holding B fixed
Z
U
MU
Z
∆
=
∆
U, Utils
∆
U
=
20
Utility function,
U
(10, Z)

∆
Z
=
1
10987654321
Z, Pizzas per semester
0
350
250
(a) Utility
230
9
, MarginalMU
Z
utility of pizza
MU
Z
10987654321
Z, Pizzas per semester
0
130
(b) Marginal Utility
20
Utility and marginal of
substitution
Lisa trades from one bundle on an
indifference curve to another by giving up
some burritos to gain more pizza
Z
B

B
MU
MRS
Z
MU
∆
==−
∆
Budget constraint
• Lisa spends all her income, Y, on pizza and
burritos
• her budget constraint is
•
p
B
B
= expenditure on B burritos
•
p
z
Z
= expenditure on Z pizzas
B
Z
pB pZ Y+=
Rewrite budget constraint
• suppose
• p
Z
= $1

• p
B
= $2
• Y = $50
• Plot this expression: Figure 4.6
Z
B
YpZ
B
p
−
=
Figure 4.6 Budget Constraint
B, Burritos
per semester
Opportunity set
50 = Y/p
Z
L
1
(p
Z
= $1, Y = $50)
25
=
Y/p
B
20
10
10030

Z, Pizzas per semester
a
b
c
d
Opportunity set
• all bundles a consumer can buy
• includes bundles on and inside the budget
constraint
10
Slope of budget constraint
• is called the marginal rate of transformation
• in our example:
Z
B
B
p
MRT
Z
p
∆
==−
∆
$1 1
$2 2
Z
B
p
MRT
p

=− =− =−
Purchasing fractional quantities
• can buy fraction quantities because axes
show a rate per time period
• effect of a change in price on consumption
One price rises
• price of pizza doubles:
p
Z
=$2 (up from $1)
• price of burritos and income unchanged
• slope of the new budget line:
MRT
= -$2/$2 = -1
• budget constraint swings in toward origin
• opportunity set shrinks
Figure 4.7a Changes in the Budget Constraint
B, Burritos
per semester
(a) Price of Pizza Doubles
Loss
50
L
1
(p
Z
= $1)
L
2
(p

Z
= $2)
25
250
Z, Pizzas per semester
Change in income
• consumer's income, Y, increases from $50 to $100
• ⇒ parallel shift out of budget line so MRT is
unchanged
• opportunity set grows ⇒ consumer can buy more
of all goods
• effectively, an increase in income is equivalent to
a comparable decrease in all prices
Figure 4.7b Changes in the Budget Constraint
B, Burritos
per semester
(b) Income Doubles
Gain
100
L
3
(Y
=
$100)
L
1
(Y
=
$50)
50

25
500
Z, Pizzas per semester
11
Budget line meets indifference
curves
• maximize utility subject to the budget
constraint
• optimal bundle, two possibilities:
• interior solution: buy some units of all goods
• corner solution: buy only one good
Interior solution
• consumer buys some units of all goods
• optimum bundle,
e
, where highest
indifference curve touches the budget line
Figure 4.8a Consumer Maximization
B, Burritos
per semester
(a) Interior Solution
Budget line
10
20
25
5030100
Z
, Pizzas per semester
I
1

I
2
I
3
d
fc
e
a
g
A
B
Tangency property
• at interior optimum, indifference curve is
tangent to budget line:
• last dollar spent on pizza gives as much
extra utility as that spent on burrito
ZZ
BB
ZB
Z
B
M
Up
M
RS MRT
MU p
MU MU
pp
=− =− =
=

Summary: Utility maximized
consumers maximize their well-being subject to
the budget constraint where
• highest possible indifference curve hits budget
constraint
• indifference curve is tangent to budget constraint
(if both goods are purchased): MRS = MRT
• last dollar spent on one good gives as much extra
utility as the last dollar spent on any other
consumed good
Optimal bundle: Corner solution
• optimal bundle at point where highest
indifference curve touches budget line
• Spenser's optimal bundle has a positive quantity
of only burritos
• reason: Spenser has flatter indifference curves
than Lisa
• indifference curve at the budget line are not
tangent at the optimal bundle
12
Figure 4.8b Consumer Maximization
B, Burritos
per semester
(b) Corner Solution
Budget line
25
50
Z, Pizzas per semester
I
1

I
2
I
3
e
Optimal bundles only on convex
sections of indifference curves
• if indifference curves are smooth, then
optimal bundles lie either
• on convex indifference curves or
• where the budget constraint hits an axis
• thus, if a consumer buys both goods,
indifference curve is convex and tangent to
budget line at optimal bundle
Figure 4.9a Optimal Bundles on Convex Sections of Indifference
Curves
B, Burritos
per semester
(a) Strictly Concave Indifference Curves
Z, Pizzas per semester
e
d
I
2
I
1
I
3
Budget
line

Figure 4.9b Optimal Bundles on Convex Sections of Indifference
Curves
e
d
I
2
I
1
B, Burritos
per semester
(b) Concave and Convex Indifference Curves
Z, Pizzas per semester
Budget
line
Solved problem
show: if the consumer buys and consumes
both goods, consumers are not satiated
(more is preferred to less)
Answer
• suppose contrary: Lisa prefers fewer burritos to
more
• show a contradiction: because burritos cost
money, she's better off consuming no burritos
• though some consumers prefer less to more at
some quantities, we do not observe consumers
making purchases where that occurs
13
Solved problem
• Alexx's firm wants to transfer him from its
SF to its Paris office

• he doesn't care where he lives, but he cares
what he eats
• firm will pay him a salary in Euros such that
he can buy the same bundle of goods in
Paris that he is currently buying
• does he benefit from moving?
Restatement
• changes: ratio of price of American meals to
price of French meals
• affects: Alexx's choice of his equilibrium
bundle and his well being
Solved Problem 4.4
French meals
per year
American meals per year
a
fL
A
L
F
I
1
I
2
Solved problem: Food stamps
Are poor people necessarily better off
receiving food stamps or a comparable
amount of cash?
Answer
• cash gives a greater choice

• whether that greater choice matters depends
on the tastes of poor people (how much
food they eat)
Figure 4.10 Food Stamps Versus Cash
All other goods
per month
YY+ 100
Y + 100
0 100
Food per month
Budget line with
food stamps
Budget line with cash
Original
budget line
A
B
f
d
e
Y
C
I
1
I
2
I
3
14
Summary: 1 Preferences

• our analysis is based on 3 assumptions:
• completeness
• transitivity
• more is better
• indifference curve map summarizes
preferences
Indifference curve properties
1. being on a higher indifference curve is better
2. indifference curves do not cross
3. there is an indifference curve through every
bundle
4. indifference curves have no thickness
5. indifference curves slope down
6. consumers purchase positive quantities only
where their indifference curves are convex to
origin
2 Utility
• utility is a numerical measure of the relative
ranking of bundles of goods
• utility is an ordinal measure
• marginal utility: extra utility from
consuming one more unit of a good holding
consumption of all other goods constant
3 Budget constraint
• consumer's opportunity set is greater, higher is
income and lower are prices
• budget constraint shows bundles that a consumer
can buy spending all income at given prices
• slope of budget line is marginal rate of
transformation (MRT): rate at which Good 1 can

be exchanged for Good 2 in the market
4 Constrained maximizing
behavior
consumers maximize their well-being subject to
the budget constraint where:
• highest possible indifference curve touches budget
constraint,
• indifference curve is tangent to budget constraint
(if both goods are purchased): MRS = MRT
• last dollar spent on one good gives as much extra
utility as last dollar spent on any other consumed
good